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Large deviations for one dimensional diffusions with a strong drift
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Voss, Jochen (2008) Large deviations for one dimensional diffusions with a strong drift. Electronic Journal of Probability, Vol.13 (No.53). pp. 1479-1526. ISSN 1083-6489.
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Abstract
We derive a large deviation principle which describes the behaviour of a diffusion process with additive noise under the influence of a strong drift. Our main result is a large deviation theorem for the distribution of the end-point of a one-dimensional diffusion with drift theta b where b is a drift function and theta a real number, when theta converges to infinity. It transpires that the problem is governed by a rate function which consists of two parts: one contribution comes from the Freidlin-Wentzell theorem whereas a second term reflects the cost for a Brownian motion to stay near a equilibrium point of the drift over long periods of time.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Stochastic differential equations, Diffusion processes, Large deviations | ||||
Journal or Publication Title: | Electronic Journal of Probability | ||||
Publisher: | University of Washington. Dept. of Mathematics | ||||
ISSN: | 1083-6489 | ||||
Official Date: | 1 September 2008 | ||||
Dates: |
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Volume: | Vol.13 | ||||
Number: | No.53 | ||||
Number of Pages: | 48 | ||||
Page Range: | pp. 1479-1526 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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